US Secretary of State Rex Tillerson shakes hands with Chinese State Councilor Yang Jiechi before their meeting at the Great Hall of the People

(POOL/AFP/File)

"There is a difference between talking and putting diplomatic pressure -- and we strongly support putting diplomatic pressure on North Korea which we're continuing to do -- but now is not the time simply to have conversations with North Korea," she said.

This would seem to contradict what Tillerson had said on Saturday, when he was asked how he would know if and when North Korea is prepared to discuss denuclearizing the Korean peninsula.

"We are probing, so stay tuned," he said.

"We ask. We have lines of communications to Pyongyang. We're not in a dark situation, a black out," he added. "We can talk to them, we do talk to them."

The State Department was quick to point out that these overtures had not revealed any sign that Kim is in fact ready for dialogue, but Tillerson had at least confirmed that channels are open.

This had been widely suspected in Washington policy circles, but by making it front-page news Tillerson seems to have irked Trump.

"The main channel is the so-called New York channel, the connection to North Korea's diplomatic mission to the UN," explained Jim Schoff, a former head of North Korea strategy at the Pentagon.

'Multiple attempts'

Washington's chief envoy for dealing with the North Korea crisis, Ambassador Joseph Yun, used this channel to Pyongyang's diplomats in New York to negotiate the release of US student Otto Warmbier -- who died after his return.

"There have been, as I understand, multiple attempts for several months by that channel to try to initiate general dialogue both on the remaining Americans held there and expressing openness to talk about denuclearization," Schoff told AFP.

Schoff, now a senior fellow at the Carnegie Endowment for International Peace, said those connections had indeed proved "unfruitful" but warned that Trump's dismissive tweets had weakened Tillerson's hand.

According to Hammond, the small number of channels of communication that are open with the North that Tillerson spoke of are being used to seek the release of the US prisoners.

"Everybody in the administration agrees with this strategy," he said. "There's no crisis between the president and Secretary Tillerson".

If that is the case -- that the channels deal only with the situation of the captives, and not with the broader issue of the nuclear standoff -- some observers will be disappointed.

Devastating war

Whatever tough talk sometimes comes from the administration, many senior US officials admit privately that there is no credible military option to disarm North Korea without provoking a devastating regional war.

In which case, Tillerson's back channels might be the best hope of a resolution.

"I certainly hope that there's some secret channel going on because I do think that there need to be discussion and understanding," said former secretary of state Madeleine Albright.

Albright is the most senior US official ever to visit North Korea. But, as Trump recalled in another tweet, US efforts to halt the North's nuclear plans have always failed.

"It's really important to lower the temperature because I'm kind of concerned about an accident of some kind that might happen and so we need to be very clear about what's going on," she said.